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1. In a large saucepan combine coffee, ketchup, Worcestershire sauce, butter, sugar, pepper, and salt. Bring to boiling, stirring occasionally; reduce heat. Simmer, uncovered, for 30 minutes, stirring frequently. Set aside 1/2 cup of the sauce. Add beef to remaining sauce in saucepan; heat through.
2. To serve, cut 1/2 inch from the tops of rolls; if desired, set tops aside. Hollow out the roll bottoms (save bread scraps for another use). Add beef mixture to the roll bottoms and spoon some of the reserved sauce over each. Top with cheese and, if desired, reserved bread tops.
3. For charcoal grill, arrange medium-hot coals around the outer edge of the grill for indirect grilling. Test for medium heat above center of grill. Place sandwiches on the grill rack in the center of the grill. Cover and grill for 5 to 10 minutes or until cheese melts. (For gas grill, preheat grill. Reduce heat to medium. Adjust heat for indirect cooking. Add sandwiches to grill rack over burner that is off. Cover and grill as above.)